A robust optimization process for a design of convertible roof module, where production uncertainty exists at all times influencing the kinematic behavior of the moving mechanism, is presented in this paper. The production uncertainty is considered as random design variables affecting the positions of joints of the moving mechanism with a certain level of uncertainty. In general, the design goals for the behavior of those mechanisms are quantitatively represented with the deviations over the total roof module movements and therefore, it is very difficult to evaluate the analytical design sensitivity as the deviations are defined by using the maximum and minimum value over the parameter intervals. Thus, this study introduces a meta-model technique to overcome the difficulties involved with the evaluation of design sensitivity. Also, the exemplary variances for the design targets are approximated from those meta-models. In addition, a sequential approximation optimization technique is used to solve a robust design problem for the convertible roof module mechanism. The robust design problem has 8 random design variables with uncertainties involved. The proposed approach requires only 87 evaluations until convergence was achieved.